In traditional Gaussian process (GP) regression, the inputs are typically assumed to be known, and uncertainty enters only through the measurements. When scalar fields are mapped using GP regression w...
arXiv:2610.03201v1 Announce Type: cross Abstract: Gaussian Processes (GPs) are a powerful tool for modelling and quantifying uncertainty in functional relationships. However, they require practitione...
arXiv:2609.25746v1 Announce Type: cross Abstract: ICP-based 3D Gaussian Splatting (3DGS) SLAM tracks in real time by registering incoming frames against map Gaussians, using each primitive's covarian...
arXiv:2608.29349v1 Announce Type: new Abstract: Gaussian process (GP) regression with a single global GP (GP-glo) incurs cubic computational cost, limiting scalability to large datasets. Product-of-e...
The paper introduces BO-pro-c, a Bayesian optimisation algorithm that employs a product-of-experts Gaussian process (GP-pro-c) as its surrogate model. GP-pro-c combines multiple local GP experts to improve uncertainty quantification, reduce computational cost, and preserve global correlations, addressing the cubic complexity of single global GP models. Experiments show that BO-pro-c achieves competitive optimisation performance with a 0.9% lower simple regret and a 39.4% reduction in computational overhead compared to a single‑global‑GP baseline.
The paper introduces SCORE, a scalable framework that learns an expressive covariance approximation for high‑dimensional Gaussian targets by combining scoring rule training with spectral‑space modeling. It decomposes the learning task into marginal distribution estimation and structured correlation matrix learning, achieving dense dependencies with linear storage and ≠(d log d) computational cost. The method employs a closed‑form Gaussian kernel score that remains valid for degenerate covariances, provides bounded gradients, and is invariant under unitary transforms, with theoretical guarantees on marginal recovery and correlation projection, and demonstrates improved performance on time‑series forecasting, monocular depth estimation, and spatial weather prediction.
The paper introduces a structured posterior‑correction framework that blends a tractable Gaussian reference with data‑driven corrections learned via diffusion models. After applying mean correction and covariance calibration, the diffusion model focuses on a low‑dimensional subspace that captures discrepancies from the Gaussian reference, while the remaining space stays Gaussian. Experiments on three scientific inference tasks show that these corrections recover hidden modes, improve sample structure, and reduce prediction error compared to the Gaussian reference, with trade‑offs between accuracy and computational cost relative to full‑field generative models.
arXiv:2511. 16340v2 Announce Type: replace Abstract: Efficient Gaussian process (GP) inference is critical for sequential decision-making tasks such as active learning, online prediction, and Bayesian optimization.
The paper presents a robust covariance estimation method for data that is both entry-wise contaminated and partially observed. It extends the Student‑t* model by using a stochastic approximation EM algorithm that operates on a reduced latent space, avoiding explicit sampling of latent Gaussian variables while maintaining a likelihood‑based framework. Experiments on synthetic and real sensor data demonstrate that this approach achieves lower Fisher‑Rao error than Gaussian, Student‑t, imputation‑based, and detect‑then‑estimate estimators, especially at moderate to high outlier rates under diffuse contamination.
arXiv:2608. 16606v1 Announce Type: new Abstract: Outliers can substantially distort Gaussian process regression (GPR) due to its conventional Gaussian observation likelihood, leading to inaccurate model learning and prediction.
arXiv:2609.16472v1 Announce Type: new Abstract: Warped Gaussian processes (GPs) handle non-Gaussian observations by mapping them into a latent standard GP via a parametric transformation called warpi...
The paper introduces GP-Refiner, a plug‑and‑play framework that uses Gaussian Process Regression to correct feature predictions in Diffusion Transformers. By observing that residuals between cached and full‑compute features follow a local zero‑mean Gaussian distribution, the method treats cached features as noisy observations of the true trajectory, enabling online correction without needing explicit labels. Experiments show that integrating GP‑Refiner with existing acceleration techniques, such as TaylorSeer, cuts computational load by 19.3% while improving image quality metrics (PSNR +0.9 dB, LPIPS 0.46→0.29).